A solid, homogeneous sphere with a mass of m 0 , a radius of r 0 and a density o

Question

A solid, homogeneous sphere with a mass of m0, a radius of r0 and a density of ?0 is placed in a container of water. Initially the sphere floats and the water level is marked on the side of the container. What happens to the water level, when the original sphere is replaced with a new sphere which has different physical parameters? Notation: r means the water level rises in the container, f means falls, s means stays the same. Combination answers like 'r or f or s' are possible answers in some of the cases.

(r, f, s, r or s, f or s, r or f or s)

1) The new sphere has a density of ? > ?0 and a mass of m < m0.
2) The new sphere has a mass of m < m0 and a radius of r > r0.
3) The new sphere has a radius of r < r0 and a density of ? > ?0

Explanation / Answer

given solid homogenoeus sphere of mass mo

radius ro

density rhoo

now the sphere floats in water and the water level is marked

original voleume of water = V

level after the sphere is immersed = V'

V' = V + immersed volume

alos

mg = immersed volume * g * rhow ( rhow is density of water)

hence

V' = V + mo/rhow

now, for a new sphere with new parameters

V" = V + m/rhow

a. rho > rhow

m < mo

hence

V" < V'

hence the waterlevel falls, f

b. m < mo and r > ro

V" < V'

hence

falls, f

c. r < ro

rho > rhoo

hence

V" = V'

the water level remainsd the same

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